On 12 March 2011, with regular goalkeeper Tobias Sippel sidelined with influenza, he made his Bundesliga debut in a 2–1 home win over SC Freiburg.[3] Trapp played all eight remaining fixtures of the season.

In 2012, he left relegated Kaiserslautern and joined promoted Eintracht Frankfurt on a four-year contract for a fee of €1.5 million.[4]

His team had a good start to his first season, sitting in third place by November, and he received plaudits for his performances against leaders Bayern Munich despite losing 2–0.[5] His campaign ended prematurely in March 2013, due to a hand injury while with the national under-21 team.[6]

By finishing sixth, Frankfurt qualified for the UEFA Europa League, and reached the last 32, where they lost on away goals to FC Porto after a 5–5 aggregate draw.[7]

Trapp made his international debut on 6 June 2017 in a 1–1 friendly draw away to Denmark, playing the full 90 minutes.[17] He was selected for the 2017 FIFA Confederations Cup in Russia later that month, which his country won, but he did not play any match.[18]

On 4 June 2018, Trapp was selected in Germany's final 23-man squad for the 2018 FIFA World Cup.[19] He was unused in a group-stage exit for the defending champions.